↑

Properties

Label 495495dy
Number of curves $4$
Conductor $495495$
CM no
Rank $0$
Graph

Related objects

Downloads

Learn more

Show commands: SageMath
Copy content sage:E = EllipticCurve("dy1") E.isogeny_class()
 

Rank

Copy content sage:E.rank()
 

The elliptic curves in class 495495dy have rank \(0\).

Complex multiplication

The elliptic curves in class 495495dy do not have complex multiplication.

Modular form 495495.2.a.dy

Copy content sage:E.q_eigenform(10)
 
\(q + q^{2} - q^{4} + q^{5} + q^{7} - 3 q^{8} + q^{10} + q^{13} + q^{14} - q^{16} + 6 q^{17} - 8 q^{19} + O(q^{20})\) Copy content Toggle raw display

Isogeny matrix

Copy content sage:E.isogeny_class().matrix()
 

The \(i,j\) entry is the smallest degree of a cyclic isogeny between the \(i\)-th and \(j\)-th curve in the isogeny class, in the Cremona numbering.

\(\left(\begin{array}{rrrr} 1 & 2 & 4 & 4 \\ 2 & 1 & 2 & 2 \\ 4 & 2 & 1 & 4 \\ 4 & 2 & 4 & 1 \end{array}\right)\)

Isogeny graph

Copy content sage:E.isogeny_graph().plot(edge_labels=True)
 

The vertices are labelled with Cremona labels.

Elliptic curves in class 495495dy

Copy content sage:E.isogeny_class().curves
 
LMFDB label Cremona label Weierstrass coefficients j-invariant Discriminant Torsion structure Modular degree Faltings height Optimality
495495.dy4 495495dy1 \([1, -1, 0, -31059, 497448]\) \(2565726409/1404585\) \(1813976537237865\) \([2]\) \(2621440\) \(1.6186\) \(\Gamma_0(N)\)-optimal
495495.dy2 495495dy2 \([1, -1, 0, -297864, -62095005]\) \(2263054145689/16769025\) \(21656658658860225\) \([2, 2]\) \(5242880\) \(1.9652\)  
495495.dy3 495495dy3 \([1, -1, 0, -107289, -140650020]\) \(-105756712489/6558605235\) \(-8470228582318217715\) \([2]\) \(10485760\) \(2.3117\)  
495495.dy1 495495dy4 \([1, -1, 0, -4757319, -3992658642]\) \(9219915604149769/511875\) \(661070166631875\) \([2]\) \(10485760\) \(2.3117\)